Physics in Motion

# Axis Theorems

### Parallel-Axis Theorem

If the moment of inertia about an axis passing through the center of mass is $$I_{CM}$$, then the moment of intertia about a parallel axis displaced by a distance $$d$$ from the cener of mass axis is:

$$I = I_{CM} + M d^2$$

### Perpendicular-Axis Theorem

The moment of inertia of a plane object about an axis perpendicular to the plane is equal to the sum of the moments of inertia about any two perpendicular axes in the plane. Thus is the $$x$$ and $$y$$ axes are in the plane,

$$I_z = I_x + I_y$$